论文标题
关于椭圆形的准式不平等现象的最小和最大解决方案图的可不同性
On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities
论文作者
论文摘要
在本说明中，我们证明了与障碍类型的椭圆形变量不平等相关的最小和最大解映射相对于强迫项和签名方向是方向区别的。在此过程中，我们表明，最小和最大溶液可以看作是某些变异不平等的溶液的单调限制，并且上述方向衍生物也可以表征为与变量不平等相关的方向衍生物序列的单调限制。我们以一些示例和热成型的应用结束了论文。
In this note, we prove that the minimal and maximal solution maps associated to elliptic quasi-variational inequalities of obstacle type are directionally differentiable with respect to the forcing term and for directions that are signed. Along the way, we show that the minimal and maximal solutions can be seen as monotone limits of solutions of certain variational inequalities and that the aforementioned directional derivatives can also be characterised as the monotone limits of sequences of directional derivatives associated to variational inequalities. We conclude the paper with some examples and an application to thermoforming.
